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Toward understanding of Quark-Gluon Plasma in relativistic heavy ion collisions. Tetsufumi Hirano Dept. of Physics The University of Tokyo. Introduction Basic Checks Energy density Chemical and kinetic equilibrium Dynamics of Heavy Ion Collisions Elliptic flow Jet quenching

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Toward understanding of quark gluon plasma in relativistic heavy ion collisions

Toward understanding of Quark-Gluon Plasma in relativistic heavy ion collisions

Tetsufumi Hirano

Dept. of Physics

The University of Tokyo


Introduction heavy ion collisions

Basic Checks

Energy density

Chemical and kinetic equilibrium

Dynamics of Heavy Ion Collisions

Elliptic flow

Jet quenching

Summary and Outlook



Physics of the qgp
Physics of the QGP heavy ion collisions

  • Matter governed by QCD, not QED

  • Frontier of high energy density/temperature

    Toward an ultimate matter (Maximum energy density/temperature)

  • Understanding the origin of matter which evolves with our universe

  • Reproduction of QGP in H.I.C.

    Reproduction of “early universe” on the Earth

History of the universe history of matter
History of the Universe heavy ion collisions ~ History of Matter

Quark Gluon Plasma



QGP study


early universe

Little bang
Little Bang! heavy ion collisions



Relativistic Heavy Ion Collider(2000-)

RHIC as a time machine!





Collision energy

Multiple production



100 GeV per nucleon


Basic checks
BASIC CHECKS heavy ion collisions

Basic checks i energy density
Basic Checks (I): Energy Density heavy ion collisions


Bjorken energy density

total energy


t: proper time

y: rapidity

R: effective transverse radius

mT: transverse mass

Critical energy density from lattice
Critical Energy Density from Lattice heavy ion collisions

Stolen from Karsch(PANIC05);

Note that recent results seem to be Tc~190MeV

Centrality dependence of energy density
Centrality Dependence of Energy Density heavy ion collisions

Well above

ec from lattice

in central

collision at RHIC,

if assuming


ec from lattice


Caveats i
CAVEATS (I) heavy ion collisions

  • Just a necessary condition in the sense that temperature (or pressure) is not measured.

  • How to estimate tau?

  • If the system is thermalized, the actual energy density is larger due to pdV work.

  • Boost invariant?

  • Averaged over transverse area. Effect of thickness? How to estimate area?

Gyulassy, Matsui(’84) Ruuskanen(’84)

Basic checks ii chemical eq
Basic Checks (II): Chemical Eq. heavy ion collisions


Resonance decay

Two fitting parameters: Tch, mB

Amazing fit
Amazing fit! heavy ion collisions

T=177MeV, mB = 29 MeV

Close to Tc from lattice

Caveats ii
CAVEATS (II) heavy ion collisions

  • Even e+e- or pp data can be fitted well!

    See, e.g., Becattini&Heinz(’97)

  • What is the meaning of fitting parameters? See, e.g., Rischke(’02),Koch(’03)

  • Why so close to Tc?

    • No chemical eq. in hadron phase!?

    • Essentially dynamical problem!

Expansion rate  Scattering rate

(Process dependent)

see, e.g., U.Heinz, nucl-th/0407067

Basic checks iii radial flow
Basic Checks (III): Radial Flow heavy ion collisions

Blast wave model (thermal+boost)

Driving force of flow

pressure gradient

Inside: high pressure

Outside: vacuum (p=0)

Sollfrank et al.(’93)

Spectrum for heavier particles

is a good place to see radial flow.

Spectral change is seen in aa
Spectral change is seen in AA! heavy ion collisions

Power law in pp & dAu

Convex to Power law

in Au+Au

  • “Consistent” with thermal + boost picture

  • Large pressure could be built up in AA collisions

O.Barannikova, talk at QM05

Caveats iii
CAVEATS (III) heavy ion collisions

  • Not necessary to be thermalized completely

    • Results from hadronic cascade models.

  • How is radial flow generated dynamically?

  • Finite radial flow even in pp collisions?

    • (T,vT)~(140MeV,0.2)

    • Is blast wave reliable quantitatively?

  • Consistency?

    • Chi square minimum located a different point for f and W

  • Flow profile? Freezeout hypersurface? Sudden freezeout?

Basic checks necessary conditions to study qgp at rhic
Basic Checks heavy ion collisions  Necessary Conditions to Study QGP at RHIC

  • Energy density can be well above ec.

    • Thermalized?

  • “Temperature” can be extracted.

    • Why freezeout happens so close to Tc?

  • High pressure can be built up.

    • Completely equilibrated?

Importance of systematic study based on dynamical framework

Dynamics of heavy ion collisions
Dynamics of Heavy Ion Collisions heavy ion collisions

Dynamics of heavy ion collisions1
Dynamics of Heavy Ion Collisions heavy ion collisions



Expansion, cooling


First contact

(two bunches of gluons)

Time scale


<<10-4(early universe)

Temperature scale 100MeV~1012K

N coll n part

y heavy ion collisions

Ncoll & Npart

Thickness function:


Gold nucleus:

r0=0.17 fm-3


d=0.54 fm

Woods-Saxon nuclear density:

# of binary collisions

# of participants

sin = 42mb @200GeV

1-(survival probability)

Centrality heavy ion collisions

Npart and Ncoll as a function of

impact parameter

PHENIX: Correlation btw. BBC and ZDC signals

Elliptic Flow heavy ion collisions

What is elliptic flow
What is Elliptic Flow? heavy ion collisions

Ollitrault (’92)

How does the system respond to spatial anisotropy?

No secondary interaction

Hydro behavior





Spatial Anisotropy


Interaction among

produced particles




Momentum Anisotropy







Time evolution of a qgp fluid
Time Evolution of a QGP Fluid heavy ion collisions





Anisotropy of energy density distribution

 Anisotropy of “Momentum” distribution

V 2 from a boltzmann simulation
v heavy ion collisions 2 from a Boltzmann simulation

Zhang et al.(’99)

ideal hydro limit

: Ideal hydro


: strongly



b = 7.5fm


generated through secondary collisions

saturated in the early stage

sensitive to cross section (~1/m.f.p.~1/viscosity)

v2 is

Schematic picture of shear viscosity
Schematic Picture of Shear Viscosity heavy ion collisions

See, e.g. Danielewicz&Gyulassy(’85)

Assuming relativistic particles,

Perfect fluid:

l=1/sr  0

shear viscosity  0

Smearing of flow

Shear flow

Next time step

Basis of the announcement
Basis of the Announcement heavy ion collisions



“Hydro limit”

response =


pT dependence

and mass ordering

Multiplicity dependence

Hydro results: Huovinen, Kolb, Heinz,…

It is found that they reproduce v2(pT) data accidentally.

T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.

Recent Hydro Results heavy ion collisions from Our Group

Bottom up approach
Bottom-Up approach heavy ion collisions

  • The first principle (QuantumChromo Dynamics)

  • Inputs to phenomenology (lattice QCD)


Non-linear interactions of gluons

Strong coupling

Dynamical many body system

Color confinement

  • Phenomenology (hydrodynamics)

  • Experimental data

  • @ Relativistic Heavy Ion Collider

    • ~150 papers from 4 collaborations

    • since 2000

Why hydrodynamics
Why Hydrodynamics? heavy ion collisions

  • Static

  • EoS from Lattice QCD

  • Finite T, m field theory

  • Critical phenomena

  • Chiral property of hadron

Once one accepts local

thermalization ansatz,

life becomes very easy.


Conserved number:

  • Dynamic Phenomena in HIC

  • Expansion, Flow

  • Space-time evolution of

  • thermodynamic variables

Dynamics of heavy ion collisions2
Dynamics of Heavy Ion Collisions heavy ion collisions



Expansion, cooling


First contact

(two bunches of gluons)

  • Inputs in hydrodynamic simulations:

  • Initial condition

  • Equation of state

  • Decoupling prescription

Centrality dependence of v 2
Centrality Dependence of v heavy ion collisions 2

TH et al. (’06).

  • Discovery of “Large” v2 at RHIC

  • v2 data are comparable with hydro results.

  • Hadronic cascade cannot reproduce data.

  • Note that, in v2 data, there exists eccentricity fluctuation which is not considered in model calculations.

Result from a hadronic cascade (JAM)

(Courtesy of M.Isse)

Pseudorapidity dependence of v 2

TH(’02); TH and K.Tsuda(’02); TH et al. (’06). heavy ion collisions

Pseudorapidity Dependence of v2


  • v2 data are comparable with hydro results again around h=0

  • Not a QGP gas  sQGP

  • Nevertheless, large discrepancy in forward/backward rapidity

  • See next slides

QGP only




Hadron gas instead of hadron fluid
Hadron Gas Instead of Hadron Fluid heavy ion collisions

T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.

A QGP fluid surrounded

by hadronic gas

“Reynolds number”

QGP core

Matter proper part:

(shear viscosity)

(entropy density)


in Hadron


in QGP

QGP: Liquid (hydro picture)

Hadron: Gas (particle picture)

Importance of hadronic corona
Importance of Hadronic heavy ion collisions “Corona”

  • Boltzmann Eq. for hadrons instead of hydrodynamics

  • Including viscosity through finite mean free path

QGP fluid+hadron gas

QGP+hadron fluids

QGP only

  • Suggesting rapid increase of entropy density

  • Deconfinement makes hydro work at RHIC!?

  •  Signal of QGP!?

T.Hirano et al.,Phys.Lett.B636(2006)299.

Qgp liquid hadron gas picture works well
QGP Liquid + Hadron Gas Picture Works Well heavy ion collisions


  • Centrality dependence is ok

  • Large reduction from pure hydro in small multiplicity events

Mass dependence is o.k.

Note: First result was obtained

by Teaney et al.

T.Hirano et al.,Phys.Lett.B636(2006)299.

Qgp liquid hadron gas picture works well contd
QGP Liquid + Hadron Gas Picture Works Well (contd.) heavy ion collisions

hybrid model


Adopted from S.J.Sanders

(BRAHMS) talk @ QM2006

How Fragile/Robust heavy ion collisions the Perfect Fluid Discovery is

1 is mass ordering for v 2 p t a signal of the perfect qgp fluid
1. Is mass ordering for v heavy ion collisions 2(pT) a signal of the perfect QGP fluid?




Mass ordering comes from

rescattering effect. Interplay btw. radial and elliptic flows

Not a direct sign of the perfect QGP fluid

Mass dependence is o.k. from


Why they shift oppositely
Why they shift oppositely? heavy ion collisions







v2 for protons can be negative

even in positive elliptic flow

must decrease with proper time

P.Huovinen et al.,PLB503,58(01)

TH and M.Gyulassy, NPA769,71(06)

Violation of mass ordering
Violation of Mass Ordering heavy ion collisions

Early decoupling from the system for phi mesons

Mass ordering is generated during hadronic evolution.

TH et al., arXiv:0710.5795[nucl-th].

2 is viscosity really small in qgp
2. Is viscosity really small in QGP? heavy ion collisions

  • 1+1D Bjorken flow Bjorken(’83)

  • Baym(’84)Hosoya,Kajantie(’85)Danielewicz,Gyulassy(’85)Gavin(’85)Akase et al.(’89)Kouno et al.(’90)…



h: shear viscosity (MeV/fm2), s : entropy density (1/fm3)

h/s is a good dimensionless measure

(in the natural unit) to see viscous effects.

Shear viscosity is small in comparison with entropy density!

A probable scenario

TH and Gyulassy (’06) heavy ion collisions

A Probable Scenario

h: shear viscosity, s : entropy density


  • Absolute value of viscosity

  • Its ratio to entropy density


Rapid increase of entropy density can

make hydro work at RHIC.

Deconfinement Signal?!

Digression heavy ion collisions

[Pa] = [N/m2]

(Dynamical) Viscosity h:

~1.0x10-3 [Pa s] (Water20℃)

~1.8x10-5 [Pa s] (Air 20℃)

Kinetic Viscosity n=h/r:

~1.0x10-6 [m2/s] (Water20℃)

~1.5x10-5 [m2/s] (Air20℃)

hwater > hair BUT nwater < nair

Non-relativistic Navier-Stokes eq. (a simple form)

Neglecting external force and assuming incompressibility.

3 is h s enough
3. Is heavy ion collisions h/s enough?

  • Reynolds number

Iso, Mori, Namiki (’59)


Perfect fluid

  • (1+1)D Bjorken solution

  • Need to solve viscous fluid dynamics in (3+1)D

  • Cool! But, tough!

  • Causality problem

4 boltzmann at work
4. Boltzmann at work? heavy ion collisions







s ~ 15 * spert !

Caveat 1: Where is the “dilute” approximation in Boltzmann

simulation? Is l~0.1fm o.k. for the Boltzmann description?

Caveat 2: Differential v2 is tricky. dv2/dpT~v2/<pT>.

Difference of v2 is amplified by the difference of <pT>.

Caveat 3: Hadronization/Freezeout are different.

5 does v 2 p t really tell us smallness of h s in the qgp phase
5. Does v heavy ion collisions 2(pT) really tell us smallness of h/s in the QGP phase?


  • Not a result from dynamical calculation, but a “fitting” to data.

  • No QGP in the model

  • t0 is not a initial time, but a freeze-out time.

  • Gs/t0 is not equal to h/s, but to 3h/4sT0t0 (in 1+1D).

  • Being smaller T0 from pT dist., t0 should be larger (~10fm/c).

6 is there model dependence in hydro calculations
6. Is there model dependence in hydro calculations? heavy ion collisions

Novel initial conditions

from Color Glass Condensate

lead to large eccentricity.

Hirano and Nara(’04), Hirano et al.(’06)

Kuhlman et al.(’06), Drescher et al.(’06)

Need viscosity and/or

softer EoS in the QGP!

Summary heavy ion collisions

  • Agreement btw. hydro and data comes from one particular modeling. (Glauber + ideal QGP fluid + hadron gas)

  • IMO, still controversial for discovery of perfect fluid QGP.

  • Check model dependences to obtain robust conclusion (and toward comprehensive understanding of the QGP from exp. data).

Heavy ion caf
Heavy Ion Caf heavy ion collisions é